If energy(E), velocity(V) and time(T) are chosen as fundamental quantities,

If Energye Velocityv And Timet Are Chosen As Fundamental Quantities Physics QuestionIf Energye Velocityv And Timet Are Chosen As Fundamental Quantities Physics Question

If energy(E), velocity(V) and time(T) are chosen as fundamental quantities, the dimensional formula of surface tension will be

Options

(a) EV⁻¹T⁻²
(b) EV⁻²T⁻²
(c) E⁻²V⁻¹T⁻³
(d) EV⁻²T⁻¹

Correct Answer:

EV⁻²T⁻²

Explanation:

Let surface tension s = EᵃVᵇTᶜ
MLT⁻² / L = (ML²T⁻²)ᵃ (L / T)ᵇ (T)ᶜ
Equating the dimension of LHS and RHS
ML⁰T⁻² = MᵃL²ᵃ⁺ᵇT⁻²ᵃ⁻ᵇ⁺ᶜ
⇒ a = 1, 2a + b = 0, -2a -b + c = -2
⇒ a = 1, b = -2, c = -2
Hence, the dimensions of surface tension are [EV⁻²T⁻²].

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